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While there are convergence guarantees for temporal difference (TD) learning when using linear function approximators, the situation for nonlinear models is far less understood, and divergent examples are known. Here we take a first step towards extending theoretical convergence guarantees to TD learning with nonlinear function approximation. More precisely, we consider the expected learning dynamics of the TD(0) algorithm for value estimation. As the step-size converges to zero, these dynamics are defined by a nonlinear ODE which depends on the geometry of the space of function approximators, the structure of the underlying Markov chain, and their interaction. We find a set of function approximators that includes ReLU networks and has geometry amenable to TD learning regardless of environment, so that the solution performs about as well as linear TD in the worst case. Then, we show how environments that are more reversible induce dynamics that are better for TD learning and prove global convergence to the true value function for well-conditioned function approximators. Finally, we generalize a divergent counterexample to a family of divergent problems to demonstrate how the interaction between approximator and environment can go wrong and to motivate the assumptions needed to prove convergence.
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Adaptive Ensemble Q-learning: Minimizing Estimation Bias via Error Feedback
The ensemble method is a promising way to mitigate the overestimation issue in Q-learning, where multiple function approximators are used to estimate the action values. It is known that the estimation bias hinges heavily on the ensemble size (i.e., the number of Q-function approximators used in the target), and that determining the 'right' ensemble size is highly nontrivial, because of the time-varying nature of the function approximation errors during the learning process. To tackle this challenge, we first derive an upper bound and a lower bound on the estimation bias, based on which the ensemble size is adapted to drive the bias to be nearly zero, thereby coping with the impact of the time-varying approximation errors accordingly. Motivated by the theoretic findings, we advocate that the ensemble method can be combined with Model Identification Adaptive Control (MIAC) for effective ensemble size adaptation. Specifically, we devise Adaptive Ensemble Q-learning (AdaEQ), a generalized ensemble method with two key steps: (a) approximation error characterization which serves as the feedback for flexibly controlling the ensemble size, and (b) ensemble size adaptation tailored towards minimizing the estimation bias. Extensive experiments are carried out to show that AdaEQ can improve the learning performance than the existing methods for the MuJoCo benchmark.
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- PAR ID:
- 10352363
- Date Published:
- Journal Name:
- AAdvances in Neural Information Processing Systems 34 (NeurIPS 2021)
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Accepted Manuscript1.0
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